This work examines the anti-plane strain elastodynamic problem for poroelastic geological media containing discontinuities in the form of cavities and cracks. More specifically, we solve for: (i) a mode III crack; (ii) a circular cylindrical cavity, both embedded in an infinite poroelastic plane; and (iii) a mode III crack in a finite-sized poroelastic block. The source of excitation in all cases are time-harmonic, horizontally polarized shear (SH) waves. These three cases depict a situation whereby propagating elastic waves are diffracted and scattered by the presence of discontinuities in poroelastic soil, and this necessitates the computation of stress concentration factors (SCF) and stress intensity factors (SIF). Thus, the sensitivity of the aforementioned factors to variations in the material parameters of the surrounding poroelastic continuum must be investigated. Bardet's model is introduced by assuming saturated soils as the computationally efficient viscoelastic isomorphism to Biot's equations of dynamic poroelasticity, and stress fields are then evaluated for an equivalent one-phase viscoelastic medium. The computational itool employed is an efficient boundary element method (BEM) defined in terms of the non-hypersingular, traction-based formulation. Finally, the results obtained herein demonstrate a marked dependence of the SIF and the SCF on the mechanical properties of the poroelastic continuum, while the advantages of the proposed method as compared to alternative analytical and/or numerical approaches are also discussed.